The core concept tested here is the understanding of double negatives in English grammar, which can sometimes be used to express a positive meaning. The correct answer is D, 'There's no way he doesn't know the answer,' which implies that he definitely knows the answer. This sentence correctly uses a double negative to affirm a positive statement. Options A, B, and C are incorrect because they misuse double negatives, leading to confusion rather than clarity. These sentences actually negate the intended positive meaning, which is a common mistake in using double negatives.